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Publisher: Oxford [u.a.] : Wiley-Blackwell × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm
    (Oxford [u.a.] : Wiley-Blackwell, 2020) Belomestny, Denis; Kaledin, Maxim; Schoenmakers, John
    In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete-time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by (Formula presented.) with (Formula presented.) being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous-time optimal stopping problems and derive the corresponding complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example. © 2020 Wiley Periodicals LLC
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    A regularity structure for rough volatility
    (Oxford [u.a.] : Wiley-Blackwell, 2019) Bayer, Christian; Friz, Peter K.; Gassiat, Paul; Martin, Jorg; Stemper, Benjamin
    A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key-stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside the scope of stochastic volatility models. On the mathematical side, Markovianity and, partially, semimartingality are lost. In this paper, we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provide a new and powerful tool to analyze rough volatility models.
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    Option pricing in the moderate deviations regime
    (Oxford [u.a.] : Wiley-Blackwell, 2017) Friz, Peter; Gerhold, Stefan; Pinter, Arpad
    We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money”) that interpolates between the well-studied cases of at-the-money and out-of-the-money regimes. First and higher order small-time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.
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    Social media reveals consistently disproportionate tourism pressure on a threatened marine vertebrate
    (Oxford [u.a.] : Wiley-Blackwell, 2020) Papafitsoros, K.; Panagopoulou, A.; Schofield, G.
    Establishing how wildlife viewing pressure is distributed across individual animals within a population can inform the management of this activity, and ensure targeted individuals or groups are sufficiently protected. Here, we used social media data to quantify whether tourism pressure varies in a loggerhead sea turtle Caretta caretta population and elucidate the potential implications. Laganas Bay (Zakynthos, Greece) supports both breeding (migratory, and hence transient) and foraging (resident) turtles, with turtle viewing representing a major component of the tourism industry. Social media entries spanning two seasons (April to November, 2018 and 2019) were evaluated, and turtles were identified via photo-identification. For the 2 years, 1684 and 2105 entries of 139 and 122 unique turtles were obtained from viewings, respectively (boats and underwater combined). However, while residents represented less than one-third of uniquely identified turtles, they represented 81.9 and 87.9% of all entries. Even when the seasonal breeding population was present (May to July), residents represented more than 60% of entries. Notably, the same small number of residents (<10), mostly males, were consistently viewed in both years; however, different individuals were targeted by boats versus underwater. Thus, turtles appear to remain in the area despite high viewing intensity, possibly indicating low disturbance. However, photo-identification records revealed a high risk of propeller and boat strike to residents (30%) leading to trauma and mortality. To reduce this threat, we recommend the compulsory use of propeller guards for all boats, compliance with speed regulations and the creation of temporary ‘refuge’ zones for resident animals at viewing hotspots, with these suggestions likely being relevant for other wildlife with similar population dynamics. In conclusion, social media represents a useful tool for monitoring individuals at a population scale, evaluating the pressure under which they are placed, and providing sufficient data to refine wildlife viewing guidelines and/or zoning. © 2020 The Authors. Animal Conservation published by John Wiley & Sons Ltd on behalf of Zoological Society of London